From 4e8b1cb8e7925cee7e6c5d0c32c1e05ad4b44c3c Mon Sep 17 00:00:00 2001
From: Andre Henriques <andr3h3nriqu3s@gmail.com>
Date: Tue, 7 Nov 2023 17:55:12 +0000
Subject: [PATCH] fix spelling

---
 cw/cw.tex | 8 ++++++++
 1 file changed, 8 insertions(+)

diff --git a/cw/cw.tex b/cw/cw.tex
index b157e43..27748ff 100644
--- a/cw/cw.tex
+++ b/cw/cw.tex
@@ -190,8 +190,16 @@
 	$$\begin{cases}
 		s  = r - h  \times a \text{ mod } q\\
 		s' = r - h' \times a \text{ mod } q
+	\end{cases} \iff
+	\begin{cases}
+		r = s + h \times a \\
+		a = \frac{s' - s}{h - h'} \land h \ne h'
 	\end{cases}
 	$$
+	therefor Alice private key $a$ is:
+	$$
+		a = \frac{s' - s}{h - h'}
+	$$
 
 	\section*{7}
 	\subsection*{7.1}